Two flasks `A` and `B` have equal volume at `100 K` and `200 K` and have `4 atm` and `1 atm` pressures, respectively. The flasks `A` contains `H_(2)` gas and `B` contains `CH_(4)` gas. The collision diameter of `CH_(4)` is twice that of `H_(2)`.
(`i`) Which of the following is true about the mean free path `(lambda)` of the molecules?
(`a`) `lambda` of `H_(2)` is twice that of `CH_(4)`.
(`b`) `lambda` of `CH_(4)` is twice that of `H_(2)`.
(`c`) `lambda` of `H_(2)` is four times that of `CH_(4)`.
(`d`) `lambda` of `CH_(4)` is four times that `H_(2)`.
(`ii`) Which of the following is true about the viscosity of the gases?
(`a`) Viscosity of `H_(2)=2xx` viscosity of `CH_(4)`
(`b`) Viscosity of `H_(2)=3xx` viscosity of `CH_(4)`
(`c`) Viscosity of `H_(2)=` viscosity of `CH_(4)`
(`d`) Viscosity of `H_(2)=(1)/(2)xx` viscosity of `CH_(4)`

Explanation

(`i`) (`b`) `lambda_(A)=(KT_(A))/(sqrt(2)pi sigma_(A^(2))P_(A)) :. lambda_(A) prop (T_(A))/(sigma_(A)^(2)P_(A))`
`:. (lambda_(A))/(lambda_(B))=((T_(A))/(T_(B)))((sigma_(B)^(2))/(sigma_(A)^(2)))((P_(B))/(P_(A)))`
`=((100)/(200))((2)/(1))^(2)((1)/(4))=(1)/(2)`
`lambda_(A)=(1)/(2) lambda_(B)` or `lambda_(B)=2lambda_(A)`
`:. lambda_(CH_(4))=2lambda_(H_(2))`
(`ii`) (`c`) `eta_(A)=((m_(A)KT_(A))^(1//2))/(pi^(3//2)sigma_(A)^(2))`, i.e., `n_(A) prop ((m_(A)T_(A))^(1//2))/(sigma_(A)^(2))`
` :. (eta_(A))/(eta_(B))=((m_(A))/(m_(B)))^(1//2)((T_(A))/(T_(B)))^(1//2)((sigma_(B))/(sigma_(A)))^(2)`
`=((2)/(16))^(1//2)((100)/(200))^(1//2)(2)/(1)^(2)=1`